\documentclass{book}
\usepackage{biblatex}

\begin{filecontents}{\jobname.bib}
@Book{Saussure:1995,
    Author    = {Ferdinand de Saussure},
    Origyear  = {1916},
    Publisher = {Payot},
    Title     = {Cours de Linguistique G{\'e}n{\'e}rale},
    Year      = {1995},
}
@Article{Thomson:1856,
  Author      = {Thomson, W.},
  Title       = {{Elements of a Mathematical Theory of Elasticity}},
  Journal     = {Philosophical Transactions of the Royal Society of London},
  Pages       = {481--498},
  Volume      = {146},
  Year        = {1856},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\begin{document}

\tableofcontents

\chapter{Chapter 1}
\cite{Saussure:1995}, \cite{Thomson:1856}, \ldots

\section{Section 1.1}

\section{Section 1.2}

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\chapter{Chapter 2}

\section{Section 2.1}

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\chapter{Chapter 3}
% The following are not listed in the actual LaTeX ToC, and as such they
% should probably not appear in the Vimtex ToC

\printbibliography
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\printbibliography[
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  title={My Bibliography}
  ]
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\printbibheading
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\end{document}
